# Lump sum annuity factor for fractional age ( years and months)

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For 415 lump sum limitation calculations, IRS says it will accept linear interpolation as a reasonable method. For example computing the maximum lump sum at age 62.45, we can use the factor for age 62 and age 63 and linear interpolation. I am looking for other acceptable methods that might provide a higher value. Can't find anything....

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I don't think you're going to find anything documented, but the only thing I can think of would be to estimate q_62.45 by assuming either UDD or constant force and interpolating between q_62 and q_63. Then calculate D_62.45 and N_62.45 to determine your annuity factor.

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I've heard that the IRS allows completed months.

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I'm interested in the approach of estimating Q62.45 by interpolating between the 2 integral ages. Have you seen this method used in a written form. Not sure I understand how that might produce a higher value than linear interpolation of the age 62-63 annuity values.

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1 hour ago, VeryOldMan said:

I'm interested in the approach of estimating Q62.45 by interpolating between the 2 integral ages. Have you seen this method used in a written form. Not sure I understand how that might produce a higher value than linear interpolation of the age 62-63 annuity values.

I can't believe it matters all that much. Doesn't it depend on the partial age? That is, for simplicity sake, if the partial ages between 0 and 1/2 then one method will give you lower overall mortality but if the partial age is between 1/2 and 1 the other method will give you lower overall mortality. I have a spreadsheet somewhere that has a selector based on either UDD or CFM but I haven't dusted it off in years.

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As I recall, you would calculate the lump sum payment using plan's definitions and administrative practice for age (complete, nearest, exact, etc.) and interpolation . Then you would convert this lump sum amount to a single life annuity and compare with the 415 \$ limit, which is the same between 62 and 65. So to convert the lump sum to a single life annuity, I would suggest to be consistent and use the same practice for age and interpolation.

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Ok thank you all. Its probably not much better that linear interpolation anyway.